AMO 2020 Primary 6 (Grade 6)

Mr Teddy had 654 dollars in the bank. He borrowed enough money to buy something for 369 dollars. That week he earned 411 dollars, paid off his debt and put the rest in the bank. How many dollars does he now have in the bank?

Find $33\times12+12\times66-66\times8-8\times33$.

Five students guessed the number of marbles in a jar: Angela 198, Bob 205, Cynthia 209, Derrick 213, Eileen 215. The closest guess wins. Two guesses were exactly 3 away from the actual number. Who won? Enter 001 for Angela, 002 for Bob, 003 for Cynthia, 004 for Derrick, or 005 for Eileen.

How many rectangles of any size can be drawn along the grid lines so that the number, or sum of the numbers, inside is divisible by 3?

In the sequence 3, 8, 13, 18, …, each term after the first is 5 more than the preceding term. What is the first three-digit multiple of 11 in the sequence?

Find the last three digits of the greatest four-digit number whose digits are strictly decreasing from left to right, whose digit sum is 18, and which is divisible by 15. For example, for 5342 you would enter 342.

Von, Kon and Fon each have a different two-digit prime number. Von has the least and Fon the greatest. Each number has digit sum 10. What is Fon’s number?

In the cryptarithm shown, different letters represent different digits from 1 through 9. If T = 5, how many possible values of PETS are there?

Find $\frac{876}{6}+\frac{874}{3}+\frac{869}{2}+\frac{43}{6}+\frac{45}{3}+\frac{50}{2}$.

A, B, C, D and E are five baseball teams. Each edge joining two teams represents one game they have played against each other. Two edges mean two games, as for A and C. How many more games has the team with the most games played than the team with the fewest?

A family has four children. Adam’s current age equals the sum of Beth’s and Carol’s current ages. Four years ago, David’s age equalled the sum of Beth’s and Carol’s ages then. Eight years ago, Adam was twice as old as David then. Beth and Carol are twins. How old is each twin now?

Write the integers 198, 199, 200, …, 498, 499 consecutively as one large number, 198199…498499. Remove all odd digits. How many digits remain?

Sally jogs from home along a straight road and travels 4 miles in one hour. She then walks in the same direction at a constant speed. After her first hour of walking she is 6.5 miles from home. How many miles from home will she be after five more hours of walking?

When $\frac1{54}$ is written as a decimal, what is the 2020th digit to the right of the decimal point?

At a supermarket, all cans of dog food have one price and all cans of cat food have another. Four cans of dog food and three cans of cat food cost 58 dollars; five cans of dog food and four cans of cat food cost 75 dollars. How many dollars does one can of dog food cost?

Identical small squares are arranged around a larger square as shown. How many rectangles are in the diagram? Count squares as rectangles.

What is the largest three-digit whole number that is a multiple of 3, one less than a multiple of 4, and one more than a multiple of 5?

How many three-digit numbers are one more than a multiple of 9, one more than a multiple of 8, and one less than a multiple of 10?

A rectangular prism has volume 480 cubic centimetres. A smaller rectangular prism is removed. Each edge of the smaller prism is half the corresponding edge of the larger one. What is the remaining volume, in cubic centimetres?

Khadijah forms a five-digit number using each of 0, 1, 2, 3 and 4 exactly once. The number is divisible by 5, 8 and 11. How many such numbers are there?